Question

A cubical room has side 4 metre. A insect that cannot fly only crawal on the walls start from one corner and move diagonally opposite corner. What is the minimum displacement covered by the insect?​

Answer 1

The ant starts at the blue/pink/green corner. He would like to get to the red/orange/grey corner.

My box is a cube; assume each side has length l. 2l is the combined width of the orange and pink faces. Using Pythag, where d is the distance the ant must travel:

d2=l2+(2l)2d2=5l2d=l5–√

Of course, for a cuboid where l≠b≠h, the values would be different. However the math would be largely the same. Assume the pink square now has dimensions l×h; the orange b×h.

d2=(l+b)2+(h)2d2=l2+2bh+b2+h2d=l2+b2+h2+2bh−−−−−−−−−−−−−−√

Note that for the cubic case, where l=b=h, the above simplifies into my original result.

Answer 2

Answer:

$\sqrt{80}$ m

Explanation:

Refer to the attachment below for a detailed explanation.